Values and variables

Vectors

Math operators

# basic arithmetic
2+2
sum_result <- 2+2
sum_result
sum_result -2
4*5
20/5

# Modulo (remainder)
5 %% 3 

# Integral division
5 %/% 3

# other common math operators and functions
4^2
sqrt(4^2)
log(2)
exp(10)
log(exp(10))

Loops

# number of iterations

n <- 100

# start loop
for (i in 1:n) {

     # BODY
  
}

# initiate variable for logical statement
x <- 1

# start loop
while (x == 1) {

     # BODY
  
}

Logical statements

2+2 == 4 # is equal to
3+3 == 7
4!=7 # is not equal to
6>3 
6<7
6<=6

Control statements

condition <- TRUE

if (condition) {
     print("This is true!")
} else {
     print("This is false!")
}

## [1] "This is true!"

\(f:X \rightarrow Y\)

\(2\times X = Y\)

Load existing functions:

# install a package
install.packages("<PACKAGE NAME>")
# load a package
library(<PACKAGE NAME>)

Functions have three elements:

1. formals(), the list of arguments that control how you call the function
2. body(), the code inside the function
3. environment(), the data structure that determines how the function finds the values associated with the names (not the focus of this course)

myfun <- function(x, y){
  
  # BODY
  z <- x + y
  
  # What the function returns
  return(z)
}

formals(myfun)

## $x
## 
## 
## $y

body(myfun)

## {
##     z <- x + y
##     return(z)
## }

environment(myfun)

## <environment: R_GlobalEnv>

Example of a function: a simple power function

powerFunction <- function(base, exponent){
  
  results <- base ^ exponent
  
  return(results)
}

powerFunction(exponent = 2, base = 3)
powerFunction(base = 2, exponent = 3)
powerFunction(2, 3)
powerFunction(c(2,4,3), 3)

apply applies a function to margins of an array or matrix. It loops over rows (MARGIN = 1) or columns (MARGIN = 2) of a matrix.

# Create an empty matrix with 2 rows and 4 columns
mymatrix <- matrix(c(1,2,3, 11,12,13, 1,10), 
                   nrow = 2, 
                   ncol = 4)
print(mymatrix)

##      [,1] [,2] [,3] [,4]
## [1,]    1    3   12    1
## [2,]    2   11   13   10

# Compute the power function of each column of the matrix

# With for-loops
for (i in 1:ncol(mymatrix)){
  print(powerFunction(mymatrix[, i], 2))
}

# With apply
apply(mymatrix, MARGIN = 2, powerFunction, exponent = 2)

lapply applies a function over a list (“list-” apply). It loops over each element of a list to execute a function.

mylist <- list(1,2,5,6,90)

# With a for loop
for (i in mylist){
  powerFunction(i, 2)
}

# With lapply
lapply(mylist, powerFunction, exponent = 2)

#####################################
# Mean Function:
# Computes the mean, given a 
# numeric vector.

meaN <- function(x){
  
}

We can use loops to simulate natural processes over time. Write a program that calculates the populations of two kinds of sloths over time. At the beginning of year 1, there are 1000 slow sloths and 1 fast sloth. This one fast sloth is a new mutation that is genetically able to use roller blades. Not surprisingly, being fast gives it an advantage, as it can better escape from predators.

A slow sloth

A fast sloth in its natural element

Each year, each sloth has one offspring. There are no further mutations, so slow sloths beget slow sloths, and fast sloths beget fast sloths. Also, each year 40% of all slow sloths die each year, while only 30% of the fast sloths do.

So, at the beginning of year one there are 1000 slow sloths. Another 1000 slow sloths are born. But, 40% of these 2000 slow sloths die, leaving a total of 1200 at the end of year one. Meanwhile, in the same year, we begin with 1 fast sloth, 1 more is born, and 30% of these die, leaving 1.4.

Enter the first year in which the fast sloths outnumber the slow sloths.

Be the function

appendsums <- function(lst){
  
    #Repeatedly append the sum of the current last three elements 
    #of lst to lst. 
}

Create a function that repeatedly appends the sum of the current last three elements of the vector lst to lst. Hint: use the append and tail functions. Your function should loop 25 times. To check if your function is correct, run:

sum_three = c(0, 1, 2)
appendsums(sum_three)

# Solution for testing:
sum_three[10] == 125